Question

Show that f is continuous on (-infinity, infinity).

f(x) = x^2 if x<1 and the square root of x if x is greater than or equal to 1.


I'm not entirely sure how to start this. Help is greatly appreciated :)

Answer 1

f(1) = 1
For x<1, the function approaches 1 as x->1 from below.
Therefore the function is continuous at x=1. It is also defined and continuous for x>1 and x<1.
Therefore it is continuous on (-infinity, infinity)

Answer 2

Many thanks!